Preheat the oven to 180 C / Gas 4. Grease a 23cm (9 in) round cake tin.
To make the cake, mix the butter and sugar together in a large bowl (I always prefer doing it with a fork or a hand whisk). Then add the yoghurt and vanilla extract and mix well.
Add the flour, bicarb and cocoa powder and mix well. Once the consistency is thick and the ingredients well blended, pour the mixture into the prepared cake tin.
Bake for 30 to 40 minutes until the cake is golden brown and a skewer inserted into the centre comes out clean. If the cake is not properly cooked through but you are happy with the colour of the top, cover the cake with tin foil and leave to bake for another 10 minutes.
Remove the cake from the oven and leave to cool for a good 30 minutes before removing from the tin. Allow the cake to cool completely before applying the icing.
To make the icing, mix the icing sugar with the lemon juice adding the lemon juice little by little and mixing with a hand whisk.
Apply the icing on top of the cake leaving 2cm around the edges of the cake free from icing as it might melt a bit. Place immediately in the fridge for the icing to harden. Once the icing is hard remove from the fridge then slice and serve.